Swept-step radar system and detection method using same

ABSTRACT

An apparatus and method for detecting an object and determining the range of the object is disclosed. A transmitter, coupled to an antenna, transmits a frequency-modulated probe signal at each of a number of center frequency intervals or steps. A receiver, coupled to the antenna when operating in a monostatic mode or, alternatively, to a separate antenna when operating in a bistatic mode, receives a return signal from a target object resulting from the probe signal. Magnitude and phase information corresponding to the object are measured and stored in a memory at each of the center frequency steps. The range to the object is determined using the magnitude and phase information stored in the memory. The present invention provides for high-resolution probing and object detection in short-range applications. The present invention has a wide range of applications including high- resolution probing of geophysical surfaces and ground- penetration applications. The invention may also be used to measure the relative permittivity of materials.

FIELD OF THE INVENTION

The present invention relates generally to detection systems andmethods, and, more particularly, to radar systems and detection methods.

BACKGROUND OF THE INVENTION

Various types of radar systems and target detection techniques areknown. Two radar systems capable of detecting a target object at arelatively short-range include the step-frequency radar and thefrequency-modulated, continuous-wave radar.

A step-frequency radar produces a carrier signal having a frequency thatis stepped by predetermined interval frequencies. Return signals areprocessed at each of the intervals or steps from which range informationis determined. Two significant limitations associated with the use of astep-frequency radar in short-range applications are its limitedunambiguous ranging capability and the significant difficulty ofimplementing range gating for short-range applications. Range gating, ingeneral terms, is a technique that improves the sensitivity of ashort-range radar by suppressing reflections up to the point of theantenna reflection. Such undesirable reflections, if left unabated,would generally render undetectable the relatively low energy returnsignals received from a short-range target object.

When a step-frequency radar is operated monostatically, for example, thereturn signal is corrupted by reflections from the antenna feed, whichsignificantly degrades the sensitivity of the system. Although rangegating for a step-frequency radar is technically implementable, veryfast switches must be employed on the transmit and receive channels togate out undesired antenna reflections. Because switching times must beon the order of nanoseconds in typical short-range applications, a rangegating implementation for a step-frequency radar which utilizes suchswitches is complex, costly, and is often unable to reliably provide forrelatively large unambiguous step frequency ranges. It is noted that therange of the step-frequency radar is limited by the number of itsfrequency steps.

Several of the problems associated with the step-frequency radar may beovercome by using a frequency-modulated, continuous-wave radar system,although this approach has associated with it a number of deficienciesand limitations that negatively impact the efficacy of such radars inshort-range applications. Although a frequency-modulated,continuous-wave radar approach offers the opportunity to implement rangegating in a generally straightforward manner and typically provides foran unambiguous ranging capability superior to that of a step-frequencyradar, the resolution of the frequency-modulated, continuous-wave radaris significantly poorer than that of a step-frequency radar.

There exists a need for a radar system and detection method thatovercomes these and other limitations associated with step-frequency andfrequency-modulated, continuous-wave radars. There exists a further needfor such a system and method that provides for accurate target detectionand range determination in short-range applications. The presentinvention fulfills these and other needs.

SUMMARY OF THE INVENTION

The present invention is directed to an apparatus and method fordetecting an object and determining the range of the object. Inaccordance with the general principles of the present invention, atransmitter, coupled to an antenna, transmits a frequency-modulatedprobe signal at each of a number of center frequency intervals or steps.A receiver, coupled to the antenna when operating in a monostatic modeor, alternatively, to a separate receive antenna when operating in abistatic mode, receives a return signal from a target object resultingfrom the probe signal. Magnitude and phase information corresponding tothe object are measured and stored in a memory at each of the centerfrequency steps. The range to the object is determined using themagnitude and phase information stored in the memory.

The present invention provides for high-resolution probing and objectdetection in short-range applications. The present invention has a widerange of applications including high-resolution probing of geophysicalsurfaces and ground-penetration applications. The invention may also beused to measure the relative permittivity of materials.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic representation of a transmit and receive signalassociated with a point target detected by a frequency-modulated,continuous-wave radar;

FIG. 2 is a block diagram illustrating a radar system in accordance withthe principles of the present invention;

FIG. 3 is a showing of center frequency shifting in accordance with aswept-step radar technique of the present invention;

FIG. 4 illustrates in flow diagram form a swept- step radar detectionmethodology in accordance with the principles of the present invention;

FIG. 5 is a top plan view of a swept-step radar system disposed in ahousing in accordance with an embodiment of the present invention;

FIG. 6 is a front plan view of the swept-step radar system housing shownin FIG. 5;

FIG. 7 is a rear plan view of the swept-step radar system housing shownin FIG. 5;

FIG. 8 is an illustration of various components and interconnections ofa swept-step radar system in accordance with an embodiment of thepresent invention;

FIG. 9 is a schematic illustration of one embodiment of thefrequency-modulated (FM) driver shown in FIG. 8;

FIG. 10 is a table of component identification and value information forthe components illustrated in FIG. 9;

FIGS. 11 and 12 illustrate an input waveform and an output waveformrespectively processed by the FM driver shown in FIG. 9;

FIGS. 13-16 illustrate various performance characteristics of theoscillator shown in FIG. 8 upon start-up and after one hour ofoperation;

FIG. 17 is a block diagram of the IF section of a swept-step radarsystem in accordance with an embodiment of the present invention;

FIG. 18 is a graphical representation of a spectrum for a targetsimulated at a distance of 5 meters (m) from a swept-step radar systemoperating in a linear sweep mode from 2 to 18 GHz;

FIG. 19 graphically illustrates the spectrum of data for a conventionalfrequency-modulated, continuous-wave radar when attempting to resolvetwo targets simulated at 5 m and 5.05 m from the frequency-modulated,continuous-wave radar, respectively;

FIG. 20 graphically illustrates the capability of a swept-step radarsystem to accurately resolve two targets simulated at 5 m and 5.05 mfrom the swept-step radar system, respectively;

FIGS. 21 and 22 illustrate the spectrum of data for a simulated singlepoint target located 20 m from a conventional frequency-modulated,continuous-wave radar and a swept-step radar, respectively;

FIGS. 23 and 24 provide comparison data demonstrating swept-step radarperformance when the frequency of the oscillator is swept the entirefrequency range of 2 to 18 GHz, and when the oscillator is swept in thelinear region of operation between 2.37 to 17.65 GHz, respectively;

FIG. 25 illustrates a configuration of a monopole antenna used incooperation with a swept-step radar system to measure the relativepermittivity of various materials;

FIGS. 26 and 27 graphically illustrate the real and imaginary parts ofmeasured and theoretical input impedance of the antenna shown in FIG.25;

FIGS. 28 and 29 are graphical illustrations of the magnitude and phaseof the reflection coefficient of an open load, and demonstrate theefficacy of a technique for calibrating a swept-step radar systememploying a monopole antenna to measure the permittivity of materials;

FIG. 30 is a graph illustrating a measurement of the relativepermittivity of a rubber sample obtained using a swept-step radarcoupled to a monopole antenna; and

FIG. 31 is a graphical illustration of a delay line measurementassociated with a swept-step radar operating in a bistatic mode.

DETAILED DESCRIPTION OF THE VARIOUS EMBODIMENTS

The present invention is directed to a high-resolution radar-typeprobing apparatus and method particularly useful in short-rangeapplications. A transmitter is employed to broadcast afrequency-modulated probe signal at each of a number of center frequencysteps. A receiver receives a return signal from which magnitude andphase information corresponding to a target object are measured andstored in a memory at each of the center frequency steps. The range tothe object is determined using the set of magnitude and phaseinformation stored in the memory.

A radar system operating in accordance with the principles of thepresent invention (referred to herein as a swept-step,frequency-modulated radar or swept-step radar) advantageously exploitsthe ranging capability of a frequency-modulated, continuous-wave radarand the high-resolution attributes of a step-frequency radar. The rangegating and frequency stepping technique in accordance with theprinciples of the present invention improves the sensitivity ofshort-range radars by eliminating deleterious antenna reflections whichheretofore have significantly reduced the sensitivity of radarsoperating at short-ranges, such as between two to three meters, forexample.

To better appreciate the advantages of the present invention, it isuseful to review the operational characteristics of a conventionalstep-frequency radar and a typical frequency-modulated, continuous-waveradar. A step-frequency radar, in general terms, transmits astep-frequency signal, V_(t)(f), such as that characterized by thefollowing equation:

V _(t)(f)=E _(o)  [1]

where, E_(o) represents the field strength of the transmit signal. Whenthe step-frequency signal travels to a target located at a distance, d,from the radar and back, the total number of wavelengths traveled isgiven by: $\begin{matrix}{N_{\lambda} = \frac{2d}{\lambda}} & \lbrack 2\rbrack\end{matrix}$

and the total angular excursion is given by:

2πN _(λ)=2βd  [3]

where, β represents the propagation constant (2π/λ). Assuming that thetransmission media is lossless and homogeneous, the return signal forthe case of a single point target is given by the following equation:

V _(r)(f)=E _(o)Γexp(j2βd)  [4]

where, Γ represents the complex reflection coefficient of the target.The expression of Equation [4] represents the case for a singlefrequency.

When the frequency is increased in uniform steps for N number of times,Equation [4] may be expanded as follows:

V _(r)(f _(n))=E_(o)Γexp j(2β_(n) d)  [5]

and $\begin{matrix}{\beta_{n} = {\frac{2\pi \quad f_{n}}{c} = \frac{2{\pi \left( {f_{o} + {n\quad \Delta \quad f}} \right)}}{c}}} & \lbrack 6\rbrack\end{matrix}$

where, f_(o) represents the start frequency, the frequency step size isrepresented by Δf, and n represents the frequency step number which isincremented between 0 to N−1. Expanding V_(r)(f_(n)) in Equation [5],the following equation is given: $\begin{matrix}{{V_{r}\left( f_{n} \right)} = {E_{o}\Gamma \quad \exp \quad {j\left( \frac{4{\pi \left( {f_{o} + {n\quad \Delta \quad f}} \right)}d}{c} \right)}}} & \lbrack 7\rbrack\end{matrix}$

From Equation [7], it can be seen that for a fixed distance, d, from theradar, the step-frequency signal, V_(r)(f_(n)), will be sinusoidal withrespect to n, with the period being determined by the parameter d. It isnoted that this equation may be viewed as representing the time seriesdata in the conventional sense. It is further noted that, with regard tothe term step-frequency radar data as used herein, the frequency domaindenotes the signal associated with V_(r)(f_(n)), and the distance(range) or time domain is associated with the spectrum of V_(r)(f_(n)).

The Fourier transform of the signal represented in Equation [7] withrespect to n will produce the spectrum of the signal corresponding tothe target and the distance, d, can then be determined. From thespectrum, the index location of the target, i, can be determined. Therelationship between the distance, d, and the index location, i, isgiven by: $\begin{matrix}{\frac{2\Delta \quad {fd}}{c} = \frac{i}{N}} & \lbrack 8\rbrack \\{d = {\frac{c}{2\Delta \quad f} \times \frac{i}{N}}} & \lbrack 9\rbrack\end{matrix}$

From Equations [8] and [9], two additional important parameters for thestep-frequency radar may be defined, namely, the maximum range and therange resolution (ΔR), as given by the following equations:$\begin{matrix}{{{Max}.{Range}} = \frac{c}{2\Delta \quad f}} & \lbrack 10\rbrack \\{{\Delta \quad R} = \frac{c}{2\Delta \quad {fN}}} & \lbrack 11\rbrack\end{matrix}$

It can be seen from Equation [10] that the maximum range for astep-frequency radar is dependent on its frequency step size (i.e., thesmaller the step size, the greater the maximum range). From Equation[11], it can be seen that for the same frequency step size, a higherresolution may be obtained by increasing the sweep bandwidth, which maybe accomplished by increasing the number of frequency steps. As will bedescribed in detail hereinbelow, the swept-step radar of the presentinvention provides for extended range determinations beyond the maximumrange defined for a step-frequency radar having equivalent operationalcharacteristics, yet maintains the same resolution.

Typically, more than one scatterer will be present in a given volumesubjected to radar probing. For purposes of example, it is assumed thatthere are K number of scatterers. Using Equation [7] above, it followsthat: $\begin{matrix}{{V_{r}\left( f_{n} \right)} = {\sum\limits_{k = 0}^{K - 1}{E_{ok}\Gamma_{k}\exp \quad {j\left( \frac{4{\pi \left( {f_{o} + {n\quad \Delta \quad f}} \right)}d_{k}}{c} \right)}}}} & \lbrack 12\rbrack\end{matrix}$

From Equation [12], it can be seen that for each frequency, f_(n), thereare K number of sinusoids with differing periods, assuming that no twoscatterers are located within the same range resolution, ΔR. In order toresolve all of the scatterers, a constraint must be imposed that only Nnumber of scatterers are present. Hence, the maximum value for K is N.The fast Fourier transform (FFT) of V_(r)(f_(n)) with respect to nprovides the spectral distribution of all the scatterers with theirassociated amplitude and phase values as given by the followingequations:

Amplitude=E_(ok)|Γ_(k)|  [13]

$\begin{matrix}{{Phase} = {\frac{4\pi \quad f_{o}d_{k}}{c} + {\arg\left( \Gamma_{k} \right)}}} & \lbrack 14\rbrack\end{matrix}$

The complex reflection coefficient of a target can be determined bycalibrating the return signal with a target of known reflectioncoefficient. The complex reflection coefficient as a function offrequency for a target can be obtained by centering a bandpass filterover the target of interest and taking the inverse fast Fouriertransform (IFFT) of the gated signal.

Having discussed the general operational characteristics of a typicalstep-frequency radar, a brief description of the operationalcharacteristics of a frequency-modulated, continuous-wave radar will nowbe provided, with reference being made to FIG. 1. In general, afrequency-modulated, continuous-wave radar frequency modulates a signal,S_(T), over some bandwidth. The bandwidth of the transmit or probesignal, S_(T), determines the range resolution. The larger the bandwidthof the probe signal, S_(T), the higher the range resolution. The returnsignal, S_(R), from a target is compared to the transmitted probesignal, S_(T), to extract the range, amplitude, and phase informationassociated with the target. The difference between the return signal,S_(R), and the probe signal, S_(T), is referred to as the intermediatefrequency (IF) signal or beat signal.

FIG. 1 is an illustration of a typical transmit and receive waveformassociated with a point target for a typical frequency-modulated,continuous-wave radar. The amount of time, τ, required for the signal totravel the two-way distance between the target and the radar, commonlyreferred to as flight time, is given by the following equation:$\begin{matrix}{\tau = \frac{2R}{c}} & \lbrack 15\rbrack\end{matrix}$

Based on the geometry of the transmit and receive waveforms, S_(T) andS_(R), illustrated in FIG. 1, a relationship may be derived between thebeat frequency, f_(b), and the range, R. The beat frequency, f_(b),represents the instantaneous difference frequency between thetransmitted and received signals, S_(T) and S_(R), respectively. For thesawtooth modulated waveform depicted in FIG. 1, the followingrelationship is given: $\begin{matrix}{\frac{\tau}{T_{m}} = \frac{f_{b}}{B}} & \lbrack 16\rbrack\end{matrix}$

Substituting for τ of Equation [15] into Equation [16], the followingequation results: $\begin{matrix}{f_{b} = \frac{2{RB}\quad f_{m}}{c}} & \lbrack 17\rbrack\end{matrix}$

where, R represents the range to the target, B represents the FM sweepbandwidth, f_(m) represents the modulation frequency of the sawtoothwaveform, c represents the speed of light, and f_(b) represents the beatfrequency.

For multiple targets, the beat signal will consist of severalfrequencies. The Fourier transform of the beat signal provides thespectral components of each of these targets. The minimum two-way traveltime, τ_(min), for the signal is given by: $\begin{matrix}{\tau_{\min} = \frac{1}{B}} & \lbrack 18\rbrack\end{matrix}$

Substituting Equation [18] into Equation [15], it can be seen that therange resolution, ΔR, for the frequency-modulated, continuous-wave radaris given as: $\begin{matrix}{{\Delta \quad R} = \frac{c}{2B}} & \lbrack 19\rbrack\end{matrix}$

From Equation [19], it can be observed that the range resolution, ΔR, isdependent on the sweep bandwidth.

It is generally understood that frequency-modulated, continuous-waveradars provide for broad-band measurements which, in turn, provide forhigh-resolution probing. This understanding is verified by Fouriertransform theory, which defines the inverse relationship between thefrequency domain and time domain: the wider the sweep bandwidth, thehigher the time resolution, hence the better resolving capabilities. Thetarget resolving capabilities of currently availablefrequency-modulated, continuous-wave radars, as with any conventionalshort-range single-antenna radar system, however, are negativelyimpacted by a number of limitations.

By way of example, typical frequency-modulated, continuous-wave radarsproduce many interference and leakage signals that are usually muchhigher in strength than the return signal, S_(R), received from atarget. Antenna reflection, for example, is a primary source ofinterference that severely limits the sensitivity of conventionalfrequency-modulated, continuous-wave radar systems when used inshort-range applications. Also, undesirable reflections from impedancemismatches between RF components contribute to an overall reduction intarget detection sensitivity and resolution. Additionally, there existsthe problem of limited isolation when the oscillator signal leaks intothe receive path. These undesirable operational characteristics severelylimit the sensitivity and resolution capabilities of conventionalfrequency-modulated, continuous-wave radars when utilized in short-range probing applications.

The radar probing apparatus and technique of the present inventionovercomes the deficiencies identified hereinabove and other knownlimitations associated with conventional short-range radar probingapproaches, yet exploits the advantageous attributes of step-frequencyand frequency-modulated, continuous-wave radar systems. A radar systemoperating in accordance with the principles of the present inventionprovides for high-resolution target detection comparable to thatprovided by a step-frequency radar and a ranging capability equivalentto that of a frequency-modulated, continuous-wave radar.

Turning now to FIG. 2, there is illustrated in system block diagram forma depiction of a radar apparatus 10 in accordance with one embodiment ofthe present invention that provides for a high-resolution range-gatedspectrum of a target object. A frequency selector 14 is coupled to atransmitter 12 that cooperatively operate to generate afrequency-modulated probe signal, S_(T), having a center frequency,f_(c). The probe signal, S_(T), is transmitted in a preferred direction,which may be in an above-ground or underground direction, using anantenna 16. A return signal, S_(R), is received by the antenna 16 andcommunicated to a receiver 18. It is note that the antenna 16 may beused in a monostatic mode or a bistatic mode, in which case a separatetransmit antenna and receive antenna are respectively coupled to thetransmitter 12 and the receiver 18.

The return signal, S_(R), is communicated from the receiver 18 to afilter 20. The filter 20 is configured to suppress undesirable antennareflection and, in one embodiment, is configured as a high-pass filterhaving a cut-off frequency selected to eliminate antenna reflection. Thefiltered return signal is then processed by a signal processor 22, suchas a digital signal processor, to determine the magnitude and phase ofthe return signal, S_(R), This information is stored in a memory 24coupled to the signal processor 22.

The frequency selector 14 then shifts the center frequency, f_(c), ofthe probe signal, S_(T), by a predetermined frequency interval or step.The probe signal, S_(T), having a shifted center frequency, f_(c), isthen transmitted by the antenna 16. The return signal, S_(R), resultingfrom the probe signal, S_(T), having a shifted center frequency, f_(c),is received by the antenna 16 and communicated to the receiver 18,filter 20, and signal processor 22 in the above-described manner. Themagnitude and phase information of the return signal, S_(R), is storedin the memory 24. The frequency selector then selects other probe signalcenter frequencies, f_(c), and the above-described process is repeatedat each of the center frequency steps. After processing the returnsignals resulting from the transmission of a probe signal produced ateach center frequency step, the signal processor 22 computes the range,R, of one or more target objects associated with the return signals.

FIG. 3 illustrates various characteristics of the probe signals producedby a swept-step radar in accordance with the principles of the presentinvention. By way of example, and not of limitation, a firstfrequency-modulated probe signal is generated at a first interval, Step1, having a center frequency, f_(C1), and an associated sweep bandwidth,BW_(S1), defined by a lower frequency limit, f_(L1), and an upperfrequency limit, f_(U1). The probe signal at Step 1 is then transmittedand a resulting return signal is processed in the above-describedmanner. A second probe signal is then generated at Step 2. The secondprobe signal has a center frequency, f_(C2), that is shifted withrespect to the center frequency, f_(C1), of the first probe signal. Thesecond probe signal has associated with it a sweep bandwidth, BW_(S2),defined by lower and upper limit frequencies f_(L2) and f_(u2),respectively.

Referring to FIG. 4, a general methodology for obtaining ahigh-resolution range-gated spectrum of a target in accordance with thenprinciples of the present invention is depicted in flow diagram form. Atstep 30, a frequency-modulated probe signal is generated and transmittedin a desired direction. A frequency-modulated return signal resultingfrom the probe signal is received at step 32. Range-gate filtering isapplied to the return signal at step 34 so as to eliminate undesirableantenna reflection which typically afflict conventional short-rangeradars. The filtered return signal is then subjected to Fouriertransformation, at step 36, which provides the magnitude and phaseresponse of any scatterers or target objects. These data are stored atstep 38.

The center frequency, f_(C), of the probe signal is then incremented or,alternatively, decremented at step 40. The probe signal having a shiftedcenter frequency, f_(C), is then transmitted, and the process defined bysteps 30 through 40 is repeated. At steps 42 and 44, the set of storedmagnitude and phase data of all scatterers or target objects issubjected to Fourier transformation to produce a high-resolutionspectral response of one or more target objects. The range to a targetobject may then be computed from this data, as will be described below.

For purpose of explanation, and not of limitation, it is assumed that anFM signal, as is defined in Equation [20] below, is transmitted by theswept-step radar at step 30 in FIG. 4:

ν_(t)(t)=A cos(2πf _(c) t+πBf _(m) t ²+θ₀)  [20]

where, f_(c) represents the center frequency, the other variables beingpreviously defined hereinabove. The received or return signal at themixer of the receiver output, as will later be described in detail, isgiven by: $\begin{matrix}{{v_{r}(t)} = {\sum\limits_{i}{{\Gamma_{i}}A\quad {\cos \left( {{2\pi \quad f_{bi}t} + {2\pi \quad f_{c}\tau_{i}} + {\pi \quad f_{bi}\tau_{i}} + \varphi_{i}} \right)}}}} & \lbrack 21\rbrack\end{matrix}$

where, |Γ_(i)| represents the magnitude of the reflection coefficient ofthe target at a location i, and φ, represents the phase of |_(i).

From Equation [21], it can be observed that at each time, t, the beatsignal, v_(r)(t), contains a summation of the scattering response fromall scatterers. Taking the fast Fourier transform of the beat signal,v_(r)(t), provides the magnitude and phase response of the scatterers ateach beat frequency. It has been determined that using a high-passfilter with a cutoff frequency slightly higher than that for the antennaplaced at the output of the mixer 77 shown in FIG. 8 suppresses anydeleterious antenna reflection.

The fast Fourier transform of v_(r)(t) is given by:

V _(fft)(f _(h))=|Γ_(fb)|exp(jψ _(fb))  [22]

where, |Γ_(fb)| represents the magnitude of the reflection coefficientof the target corresponding to the beat frequency, f_(b), and:

ψ_(fb)=2πf _(c)τ_(fb)+φ_(fb)  [23]

where, τ_(fb) represents the two-way flight time to the scatterer andback, and φ_(fb) represents the phase of Γ_(fb).

At the beat frequency, f_(b), corresponding to the target, the spectrumwill contain the amplitude and phase information of the targetcorresponding to the center frequency, f_(c). For each step of thecenter frequency, f_(c), the amplitude and phase information of thetarget is stored. A set of step-frequency radar data is thus producedand is given by the following equation:

H(i)=|Γ_(tar)|exp{j(2πf _(i)τ_(tar)+φ_(tar))}  [24]

where, f_(i)=f_(o)+iΔf, and Δf represents the frequency step size. Byexpanding Equation [24], the following equation results:

H(i)=|Γ_(tar)|exp{j(2πf _(o)τ_(tar) +2πΔfτ _(tar) i+φ _(tar))}  [25]

Taking the fast Fourier transform of H(i) with respect to i provides thehigh-resolution spectral response of the target.

The range, R, to the target may be computed in the following manner. Thetime resolution (Δt) associated with a step-frequency probing techniqueis given by: $\begin{matrix}{{\Delta \quad t} = \frac{1}{N\quad \Delta \quad f}} & \lbrack 26\rbrack\end{matrix}$

where, N represents the number of frequency steps. Substituting Δt for tand ΔR for R in Equation [15] provided hereinabove, the relationshipbetween the range resolution and time resolution is given by:$\begin{matrix}{{\Delta \quad R} = \frac{\Delta \quad t \times c}{2}} & \lbrack 27\rbrack\end{matrix}$

It can be seen that the index location of the target, i, is equal toΔfτ_(tar), which varies from 0 to N−1, where N represents the number offrequency steps. Thus, the range, R, to the target may be computed as:

R=ΔRΔfτ_(tar)  [28]

Referring now to FIGS. 5-8, there is illustrated an embodiment of aswept-step radar apparatus that operates in accordance with the radarprobing methodology depicted in FIG. 4 and the principles represented inmathematical terms in Equations [20] through [28]. The swept-step radar50 includes a waveform generator 54 and an FM driver 56 coupled to thewaveform generator 54. The RF section 58 of the swept-step radar 50includes a YIG oscillator 60 coupled to both the FM driver 56 and a 6-dBcoupler 62, a dual directional coupler 64 coupled to the 6-dB coupler62, a phase trimmer (not shown), a dual mixer 77, and a coaxial switch70 that selectively couples a single antenna 66 or a dual antennaapparatus 66/68 to an input of the dual mixer 77.

An IF section includes two IF amplifiers 76 and 78 which arerespectively coupled to first and second mixers 72 and 75 of the dualmixer 77. The first and second IF amplifiers 76 and 78 are respectivelycoupled to an incident channel 80 and a reflected channel 82. As willlater be described in detail, a highpass filter 74 is placed in thereflected channel 82 between the second IF amplifier 78 and the secondmixer 75 of the dual mixer 77 to effectively eliminate undesirableantenna reflection.

The waveform generator 54, in accordance with one embodiment of thepresent invention, produces a sawtooth waveform, such as thatillustrated in FIG. 1. A MAX038 High-Frequency Waveform Generator,manufactured by Maxim Integrated Products, produces a sawtooth waveformof a type suitable for use in this embodiment of the present invention.The MAX038 waveform generator is a high-frequency function generatorcapable of producing accurate triangle, sine, and square waveforms byconfiguring the appropriate jumper settings. The sawtooth waveform maybe generated by changing the duty cycle of the triangular waveform. TheMAX038 waveform generator, as assembled in the factory, generateswaveforms from 325 kHz to 10 MHz.

The frequency range for the generated waveform may be set by selectingthe appropriate capacitor (C1) value from the table provided on page 4of the MAX038 1994 data sheet. The frequency of the generated waveformmay then be set by adjusting the potentiometers, IIN or FADJ. Themodulation frequency was chosen based on the range of operation. Inaccordance with this embodiment, a 1-kHz modulation was selected toenable operation at ranges up to 29 m with a maximum beat frequency of25 kHz and a sweep bandwidth of 130 MHz (see Equation [17] above).

The center frequency, f_(C), of the YIG oscillator 60 may be deviated asmuch as +/−70 MHz by pumping current into the FM coil of the YIGoscillator. The sensitivity of the FM coil is given as 450 kHz/mA.Theoretically, in order to achieve a sweep bandwidth of 140 MHz, as muchas +/−155.6 mA of current must flow into the FM coil. This amount ofcurrent is well within the maximum current rating threshold of +/−200 mAspecified by the manufacturer.

The FM driver 56 was initially designed to produce a current of +/−155.6mA. However, upon testing the FM driver 56 with the spectrum analyzer,it was found that this amount of current produced center frequencydeviations of only +/−55 MHz. The current flow into the FM coil was thenincreased to +/−190 mA to deviate the center frequency of the YIGoscillator 60 by +/−65 MHz. Hence, a range resolution of 1.15 m isobtained for a sweep bandwidth of 130 MHz.

The schematic diagram of FIG. 9 is a depiction of an exemplary FM driver56 for use in the embodiment of the swept-step radar 50 illustrated inFIGS. 5-8. In the diagram of FIG. 9, resistor R₁ and inductor L₁represent the input impedance of the FM port coupled to the YIGoscillator 60. Transistors Q₁ are configured as a PNP Darlingtontransistor pair that supplies current from 0 to 380 mA to the FM port.The Q₁ Darlington transistor pair is designed to supply 380 mA ofcurrent in response to an input voltage of +2 V, and 0 mA of current inresponse to an input voltage of −2 V. This is accomplished by selectingappropriate values for resistors R₂ and R₅ of the difference amplifierAMP₁. The variable resistor, POT₁, is used to fine tune the currentrange to be 380 mA. As such, the bandwidth of the FM sweep of the YIGoscillator 60 may be adjusted using POT₁.

Amplifier AMP₄ acts as a buffer that drives the Q₁ Darlington transistorpair. The voltage appearing at the positive terminal of AMP₁ may beadjusted using the variable resistor POT₂ in order to accurately controlthe current within the range of 0 to 380 mA. Hence, POT₂ operates as anFM bandwidth offset adjuster. Diode D₁ is a 10 V zener diode thatprovides a stable +10 V supply. This voltage is used as a referencevoltage for POT₂ to set the offset voltage at the positive terminal ofAMP₁, and is also used as the input voltage to AMP₂ for setting thereference voltage at resistor R₁₄.

Transistors Q₂ are configured as an NPN Darlington transistor pair thatpulls a constant +190 mA current out of the FM port. This effectivelysupplies +/−190 mA to the FM port. To achieve this, the voltage acrossthe 22 ohm resistor R₁₄ is designed to be about 4.2 V. This voltage dropacross resistor R₁₄ will result in 190 mA of current in the emitter ofthe Q₂ transistor pair. Since the common-emitter current gain for theDarlington configuration is very large (e.g., β=2,500), the current inthe collector of Q₂ can also be assumed to be about 190 mA. Because ofthe large wattage generated across resistors R₉ and R₁₄, which is about1W, 3W rated resistors are suitable for withstanding this high wattage.

The op-amp AMP₂ is an inverting amplifier that provides the referencevoltage across the resistor R₁₄. The values of the resistors R₆ and R₁₁are selected to obtain the required voltage at R₁₄, and POT₃ is avariable resistor that can be used to fine tune the reference voltage atR₁₄. Operational amplifier AMP₃ is a buffer amplifier that drives thebase of the Q₂ Darlington transistor pair. The values for the componentsshown in FIG. 9 are provided in tabular form in FIG. 10.

The circuit illustrate in FIG. 9 was simulated using the computerprogram known as Electronics Workbench to verify the operation of the FMdriver 56. The results of the simulation are shown in FIGS. 11 and 12.FIG. 11 is a showing of the input triangle waveform, which variesbetween −0.1 V and +0.1 V . FIG. 12 is a showing of the output at the FMport, which varies between −2 V and +2 V. This voltage variationcorresponds to an effective current ranging between −200 mA and +200 mAacross a 0.5 ohm resistor.

Returning now to FIGS. 5-9, the RF section of the swept-step radar 50operates in the 2 to 18 GHz frequency range. The RF section isresponsible for transmitting and receiving the range-gated FM signal. Adigital-tuned YIG oscillator 60 is employed as the signal source for theRF section. The center frequency, f_(c), is stepped by sending controlbits from a processor, such as an on-board processor or a personalcomputer, to the digital driver of the oscillator 60 via a CIODIO-24control board, for example. In this configuration, there are 12 controlbits used to determine the center frequency, f_(c), with 0_(h) andFFF_(h), represented in hexadecimal form, corresponding to 2 and 18 GHz,respectively. Each control bit corresponds to a frequency resolution asdetermined by the following Equation: $\begin{matrix}\begin{matrix}{{\Delta \quad f} = \frac{\left( {18 - 2} \right)\quad {GHz}}{\left( {{FFF}_{h} - 0} \right)}} \\{= \frac{16\quad {GHz}}{4095}} \\{= {3.9072\quad {MHz}}}\end{matrix} & \lbrack 29\rbrack\end{matrix}$

It is understood that the operational frequency range of the swept-stepradar, as well as the frequency step size, number of steps, and otherparameters, may be varied as needed depending on the requirements of aparticular application. Table 1 below provides values for the variousoperational parameters of the swept-step radar in accordance with oneembodiment of the present invention. The values presented in Table 1 areprovided for purposes of explanation and not of limitation.

TABLE 1 PARAMETER VALUE Center Frequency 2.37-17.65 GHz Center FrequencyStep Size 11.7 MHz Number of Frequency Steps 1300 RF Bandwidth 130 MHzRange Resolution 1.15 m Max. IF Frequency 25 kHz Sampling Frequency 50kHz Max. Unambiguous Range 29 m Number of Sweeps Averaged 1 Number ofSamples per Sweep 50 samples

To determine the accuracy of the given frequency resolution, tests wereperformed on the YIG oscillator 60 using a spectrum analyzer. Thespectrum analyzer was controlled by a PC via an HPIB board, and the YIGoscillator 60 was stepped through the entire 4096 frequencies. At eachfrequency, the output power from the test port 86 of thedual-directional coupler 64, shown in FIG. 5, and the actual frequencyof the YIG oscillator 60 were recorded. The graphs in FIGS. 13-16 showthe actual frequency step size of the oscillator 60 and the deviation ofthe frequencies from their straight-line fit after one hour ofoscillator operation.

Ideally, the plot in FIGS. 13 and 14 should have zero standarddeviation, but a standard deviation on the order of 0.12 MHz isobserved. The standard deviation exhibited a slight drop with anincrease in time. It can be observed from FIGS. 15 and 16 that thedeviation at the edges of the frequency span is fairly high anddecreases as a function of time. This indicates that the temperature ofthe oscillator 60 needs to stabilize in order to obtain optimumperformance. As will later be discussed, results from computersimulations demonstrate that the oscillator 60 should be operated in thelinear region in order to avoid aliasing of the signal. It is thereforedesirable to operate the swept-step radar between 2.37 GHz and 17.65GHz, rather than between 2 and 18 GHz in accordance with this embodimentof the present invention. It is reiterated that the frequency range ofswept-step radar operation may vary from that described herein dependingon a given application. By way of example, frequencies below 2 GHz maydefine the lower bound of the operational frequency range, while theupper bound may exceed 18 GHz.

The 6-dB directional coupler 62, shown in FIG. 8, supplies one-fourth ofthe output power from the YIG oscillator 60 to the local oscillator (LO)port 73 of the dual mixer 77 for down converting the RF signal from theincident and reflected channels 80 and 82, respectively. The remainingpower is coupled to the input port 84 of the dual-directional coupler64. A suitable dual-directional coupler is model HP 772D manufactured byHewlett-Packard. The input signal applied to the input port 84 of thedual-directional coupler 64 is derived from the 6-dB coupler. A fractionof this signal (e.g., −20 dB) is coupled to the test port 86 formeasurement, and the remaining signal content is coupled to the incidentport 80.

The signal from the incident channel 80 is used as a calibration signalto remove system effects. This is achieved by matching the phase of thesignals from the incident channel 80 and reflected channel 82 byintroducing a sub-delay line 71 between the incident channel 80 and theRF input of the dual mixer 77. The length of the sub-delay line 71 ischosen to ensure that the returns from the incident channel 80 and thereflected channel 82 arrive at the input terminals of the dual mixer 77substantially at the same time. A phase trimmer (not shown) isintroduced between the sub-delay line 71 and the dual mixer 77 toprovide for fine tuning when matching the phase of the returns from theincident and reflected channels 80 and 82, respectively.

The dual mixer 77, as previously mentioned, is used to down convert theRF signal to an IF signal on both the incident and reflected channels 80and 82. The output from the YIG oscillator 60 is used as the localoscillator (LO) to down convert the RF signal. The YIG oscillator'sminimum output power is 15 dBm, and one-fourth of 15 dBm is 9 dBm.Hence, for a local oscillator power of 9 dBm, the conversion loss forthe dual mixer 77 is 6.5 dBm. A coaxial switch 70 is used to selectivelyperform either single antenna (S₁₁) 66 or dual antenna (S₂₁) 66/68 radarmeasurements. The coaxial switch 70 is driven by a −15 V source toprovide for switching between the S₁₁ and S₂₁ modes of operation.

Turning now to FIG. 17, there is illustrated in block diagram form anembodiment of the IF section of a swept-step radar. The IF section isresponsible for amplifying the down-converted RF signal coming from thedual mixer 77. The IF section includes a 4-kHz high-pass filter 102 andan IF amplifier 101. The RF signal, which has been down-converted by themixer 77, is fed to the high-pass filter 102 to cut off leakage signalsand reflection from the test port 86 and the antenna 66 and/or 68. Theoutput of the high-pass filter 102 is then fed to the input of the IFamplifier 101.

The IF amplifier 101 comprises three stages to amplify the signal to therequired gain level. The first stage is a single-pole high-pass filter104 with a fixed gain of 30 dB implemented with an op-amp. The secondstage is a programmable gain amplifier 106 with gains of 0, 20, 40, and60 dB. The gain of the amplifier 106 is set by sending the appropriategain control bits from a processor or from a computer to theprogrammable gain amplifier 106 via a CIODIO-24 I/O board, for example.The final stage is a unity-gain buffer 108 used to boost the outputcurrent of the programmable gain amplifier 106 to a level sufficient fordriving a 50 ohm load.

In accordance with one embodiment of the present invention, dataacquisition is performed by digitizing the IF signal at the output ofthe IF amplifier 101 using a high-speed analog-to-digital convertor(A/D) board. A suitable A/D board to digitize the IF signal is modelRTI-860 manufactured by Analog Devices. The RTI-860 A/D board is capableof sampling at a frequency of 250 kHz with 12-bit resolution insingle-channel mode, and up to 200 kHz in a multi-channel mode. Samplingrates of up to 330 kHz in single-channel mode and 250 kHz inmulti-channel mode can be achieved using 8-bits of resolution. For N-bitresolution, the maximum signal-to-noise ratio (SNR) that can be measuredis given by the following equation:

SNR _(max) ˜t 6×(N−1)−1.25(dB)  [30]

Hence, for 8-bit resolution, the maximum SNR that can be measured is40.75 dB, and for 12-bit resolution, the maximum measurable SNR is 64.75dB.

An input voltage range of either +/−5 V or 10 V may be selected usingthe appropriate jumper. The digitized data can be stored in eitheron-board memory or system memory. The RTI-860 has 256K×12 bits ofdynamic RAM (DRAM) for storing the acquired data without beinginterrupted by the computer's CPU. Three methods of triggering A/Dconversion with the RTI-860 are available. These include digital,analog, and software triggering.

Digital signal triggering is a type of edge triggering that uses anexternal digital signal. The RTI-860 can be configured to trigger viasoftware on either the falling edge or on the rising edge of theexternal digital signal. Analog triggering is accomplished by comparingan external analog input signal with a software-specified thresholdvoltage. The RTI-860 can be configured via software to trigger when theanalog signal is above or below the specified threshold voltage.Software triggering initiates the A/D conversion process as soon as theuser or host requests data.

In one embodiment, a sampling rate of 200 kHz with 12-bit resolution inmulti-channel mode is selected, which effectively provides for a 50 kHzper channel sampling rate since there are a total of four channels. Thetrigger mechanism is a rising-edge digital-signal trigger that issynchronized to the sawtooth waveform. The digitized data are firststored in on-board DRAM and then transferred to system memory. The dataacquisition program may be written in C language and, if desirable,interfaced with MATLAB software for purposes of performing dataprocessing.

The advantages of the swept-step radar probing apparatus and method inaccordance with the present invention and as described herein weredemonstrated and verified by use of a MATLAB simulation approach. Forpurposes of concept verification, several operating scenarios weresimulated, as are described below in Examples 1 through 5.

EXAMPLE 1

FIG. 18 is a graphical representation of a spectrum for a targetsimulated at a distance of 5 m from the swept-step radar operating in alinear sweep mode from 2 to 18 GHz. The plot of the spectrum data inFIG. 18 demonstrates unambiguous and accurate detection of the simulatedtarget located at 5 m from the swept-step radar.

EXAMPLE 2

FIGS. 19 and 20 dramatically illustrate the high-resolution capabilityof the swept-step radar operating in accordance with the principles ofthe present invention in comparison to that provided by a conventionalfrequency-modulated, continuous-wave radar. FIG. 19 graphicallyillustrates the spectrum of data for a conventional frequency-modulated,continuous-wave radar when attempting to resolve two targets simulatedat 5 m and 5.05 m from the radar, respectively. It can be seen from theplot in FIG. 19 that the conventional frequency-modulated,continuous-wave radar was unable to accurately resolve the two, closelyspaced targets. Rather, the frequency-modulated, continuous-wave radardata suggests the presence of only a single target.

In stark contrast, as is illustrated in FIG. 20, the plot of spectrumdata demonstrates that the swept-step radar clearly resolves the twotargets simulated at 5 m and 5.05 m from the swept-step radar, whichrepresents a separation distance of only 5 cm. It is noted that both thefrequency-modulated, continuous-wave and swept-step radars weresimulated so as to operate in a linear sweep mode from 2 to 18 GHz.

EXAMPLE 3

The data graphically presented in FIGS. 21 and 22 demonstrate that therange of the swept-step radar is co-extensive with that of aconventional frequency-modulated, continuous-wave radar. FIG. 21illustrates the spectrum of data for a simulated single point targetlocated 20 m from a conventional frequency-modulated, continuous-waveradar. FIG. 22 illustrates that the range of the swept-step radar isequivalent to that of the frequency- modulated, continuous-wave radar.

Previously, by using a network analyzer as a step-frequency radar,targets beyond 15 m could not be detected, which is a range limitdetermined by the number of points and the sweep bandwidth. As such, thespectrum obtained by the swept-step radar is simply wrapped around, andthe corrected range, or actual range, can be determined from the plotshown in FIG. 22 by adding 15 m to the displayed range. As such, theswept-step radar, taking into account the additional 15 m offset (15 m+5m=20 m), accurately detects the presence of the target located 20 m fromthe swept-step radar.

EXAMPLES 4 & 5

FIGS. 23 and 24 provide comparison data demonstrating swept-step radarperformance when the frequency of the oscillator 60 is swept the entirefrequency span of 2 to 18 GHz (FIG. 23), and when the oscillator 60 isswept in the linear region of operation from 2.37 to 17.65 GHz (FIG.24). It can be seen in these figures that degradation in the performanceof the radar results when the frequency steps of the oscillator 60 arenot uniform. The linearity of the sweep was determined by measuring theoscillator's actual frequency and removing the straight-line fit fromthese frequencies. The results of these measurements were discussedpreviously in connection with the description of the YIG oscillator.

An advantageous feature of the swept-step radar in accordance with theembodiment of the invention shown in FIGS. 5-7 concerns the portablityof the system, which is particularly advantageous when performingmaterial permittivity measurements, for example. Obtaining accuratepermittivity measurements using known techniques is achieved withoutnecessity of relatively bulky network analyzer equipment, which isgenerally required when employing a conventional permittivity measuringsystem.

To facilitate permittivity measurements using a swept-step radar whichoperates in accordance with the principles of the present invention, acylindrical monopole antenna apparatus 120, an embodiment of which isillustrated in FIG. 25, was constructed. It is noted that a knownpermittivity measurement technique involves the use of a flat-plateantenna for radiating a single-frequency probe signal. In order tomeasure the relative permittivity of a material accurately, it isdesirable that the material be disturbed as little as possible duringtesting. It is noted that the monopole antenna apparatus 120 wasselected because of the ease by which this antenna configuration may beused when preparing the sample material for permittivity measurementtesting. Only one hole, having a length equal to that of the monopoleantenna 122, needs to be drilled into the sample material in order toimmerse the antenna 122 into the medium.

In modeling the input impedance of the monopole antenna 122, an antennalength (h) was selected, and a diameter (d) was then determined suchthat the antenna input reactance was zero. It was determined that theratio of length (h) to diameter (d) should be at least 10 in order toobtain the desired resonation characteristic. The length (h) of themonopole antenna 122 at the first resonant frequency is given by thefollowing equation: $\begin{matrix}{h = {\frac{0.24c}{f} - \frac{d}{2}}} & \lbrack 31\rbrack\end{matrix}$

The length (h) of the antenna 122 was determined to be 5 mm, and thediameter (d) was determined to be 0.5 mm, based on a resonant frequencyof 14 GHz and an h/d ratio of 10. A larger h/d ratio may be desirable interms of modeling the input impedance but, in practice, larger h/drations would result in a smaller antenna diameter and, hence, a thinnerantenna. A thinner antenna may be impractical because drilling narrowholes into sample material may be difficult, and the antenna may besubject to frequent breakage. The measured and theoretical inputimpedance in free space calculated using a conventional moment methodare shown in FIGS. 26 and 27. FIG. 26 shows the real part of the antennainput impedance, while FIG. 27 illustrates the imaginary part of theantenna input impedance.

The radiation efficiency of the antenna system 120 depicted in FIG. 25is dependent in part on the ground plane 124 of the antenna apparatus120. In general, the radius of the ground plane 124 should be at least aquarter wavelength at the lowest operating frequency. Since, inaccordance with one embodiment, the lowest operating frequency is 2 GHz,a suitable ground plane should be constructed to have a diameter of 7.54cm.

In order to measure the relative permittivity of materials using themonopole antenna apparatus 120 shown in FIG. 25, the input impedance ofthe antenna 120 in the measured medium is to be determined. Therelationship between the input impedance (Z) of the antenna 120 in amedium and the reflection coefficient (Γ) of the medium is given by thefollowing equation: $\begin{matrix}{{Z\left( {\omega,ɛ} \right)} = {Z_{0}\frac{1 + {\Gamma \left( {\omega,ɛ} \right)}}{1 - {\Gamma \left( {\omega,ɛ} \right)}}}} & \lbrack 32\rbrack\end{matrix}$

where, Z₀ represents the characteristic impedance of the transmissionline (i.e., 50 ohm).

Deschamps' theorem states that for a short monopole antenna, therelationship between the input impedance of the antenna immersed in twomediums with different permittivity is given by:

{square root over (ε_(r1)+L )}Z ₁(ω₁, ε_(r1))={square root over(ε_(r2)+L )}Z ₂(ω₂, ε_(r2))  [33]

It is understood that the input impedance of the antenna 120 can bemodeled in terms of the complex wave number, k, and the physical lengthof the antenna, h, by a rational function. The normalized inputimpedance is given as: $\begin{matrix}\begin{matrix}{{Z_{n}({kh})} = \quad {\sqrt{ɛ_{r}}{Z\left( {\omega,ɛ_{r}} \right)}}} \\{= \quad {\frac{kh}{k_{o}h}{Z\left( {\omega,ɛ_{r}} \right)}}}\end{matrix} & \lbrack 34\rbrack\end{matrix}$

where, k_(o) represents the wavenumber in free space (2π/λ), andZ_(n)(kh) represents the normalized input impedance that can be modeledby the following rational function of order m+1: $\begin{matrix}{{Z_{n}({kh})} \approx {j{\frac{K}{kh}\left\lbrack \frac{1 + {{jb}_{1}({kh})} + {b_{2}({kh})}^{2} + {{jb}_{3}({kh})}^{3} + \ldots + {b_{m}({kh})}^{m}}{1 + {{ja}_{1}({kh})} + {a_{2}({kh})}^{2} + {{ja}_{3}({kh})}^{3} + \ldots + {a_{m}({kh})}^{m}} \right\rbrack}}} & \lbrack 35\rbrack\end{matrix}$

This model assumes the presence of antenna resonance. Accordingly, it isconsidered desirable that the antenna 120 be designed so that the ratioof the antenna length (h) to the diameter (d) (i.e., h/d) is greaterthan ten.

To determine the relative permittivity of materials, the followingprocedure may be employed. Initially, the input impedance of antenna 120in air is determined. These data are used to determine the coefficientsin Equation [35] above. For a third order rational function, analgebraic solution is given for the coefficients. The input impedance ofthe antenna is then measured in the material. The value of kh is thendetermined using Equations [33] and [34]. It is noted that the data arevalid over the frequency range where |kh|<=k_(o)h|_(res). Finally, therelative permittivity, ε_(r), is determined by: $\begin{matrix}{ɛ_{r} = \left( \frac{kh}{k_{o}h} \right)^{2}} & \lbrack 36\rbrack\end{matrix}$

The accuracy of the relative permittivity is dependent on the accuracyof the measurement of the reflection coefficient. To obtain accuratemeasurement of the reflection coefficient at the test port 86, thesystem should be calibrated up to the point of measurement. A suggestedcalibration approach can be described by the equations below:$\begin{matrix}{{H(f)} = \frac{- 1}{S(f)}} & \lbrack 37\rbrack\end{matrix}$

Γ_(M)(f)=H(f)×M(f)  [38]

where, S(f) represents the measured reflection from the short circuitload, H(f) represents the calibration factor, M(f)represents themeasured reflection from the medium, and Γ_(M)f(f) represents the truereflection from the medium.

The system may be calibrated by measuring the reflection coefficient ofthe short circuit, S(f), at the test point. The calibration factor,H(f), is obtained by dividing the true reflection of the short circuitload, which is −1, by S(f). This function, H(f), is multiplied by themeasured reflection from the medium to obtain the true reflection fromthe medium, Γ_(M)(f). FIGS. 28 and 29 demonstrate the accuracy of thiscalibration technique. Using this technique, the reflection coefficientof an open load (Γ_(open)=1) with less than 2% error in magnitude (FIG.28) and less than 3% error in phase (FIG. 29) across the frequency rangemay be obtained.

FIG. 30 shows the relative permittivity of a rubber sample obtainedusing a monopole antenna in accordance with the above-discussedprocedure. The theoretical relative permittivity is given as 3 for thereal part and 0 for the imaginary part. FIG. 30 demonstrates closeagreement between the empirically determined permittivity of the rubbersample through use of the monopole antenna 120 and the theoreticallyderived permittivity value. It is noted that FIG. 31 illustrates theresults of a delay line measurement made in the S₂₁ mode of operationwith 0-dB gain.

It is believed that the performance of the swept-step radar may befurther improved by linearizing the frequency steps by using a directdigital synthesizer (DDS). It is further believed that the IF spectrumcan be further improved if the IF signal is weighted by a window, suchas a Hamming window, before it is input into the range gating filter toreduce the effects of ringing.

It will, of course, be understood that various modifications andadditions can be made to the various embodiments discussed hereinabovewithout departing from the scope or spirit of the present invention.Accordingly, the scope of the present invention should not be limited bythe particular embodiments described above, but should be defined onlyby the claims set forth below and equivalents thereof.

What is claimed is:
 1. A method of detecting an object, comprising: (a)transmitting a probe signal having a center frequency and a sweepbandwidth; (b) receiving a return signal resulting from the probesignal; (c) storing information corresponding to the object derived byusing the return signal; (d) shifting the center frequency; (e)repeating steps (a) through (d) a number of times; and (f) determining arange to the object using the stored information.
 2. The method of claim1, wherein storing the information comprises storing magnitude and phaseinformation corresponding to the object derived by using the returnsignal.
 3. The method of claim 2, wherein determining the rangecomprises determining the range to the object using the stored magnitudeand phase information.
 4. The method of claim 1, wherein the probesignal comprises a frequency-modulated probe signal.
 5. The method ofclaim 1, wherein shifting the center frequency comprises shifting thecenter frequency within a frequency range of approximately 2 GHz toapproximately 18 GHz.
 6. The method of claim 1, wherein shifting thecenter frequency comprises changing the sweep bandwidth.
 7. The methodof claim 1, wherein shifting the center frequency further compriseslinearizing a plurality of frequency steps over which the centerfrequency is shifted.
 8. The method of claim 1, further comprisingrange-gate filtering the return signal.
 9. The method of claim 1,wherein determining the range further comprises determining the range ofthe object where the object is situated less than approximately 3 metersrelative to a location at which transmitting the probe signal occurs.10. The method of claim 1, wherein the object is an underground object.11. The method of claim 1, wherein transmitting the probe signalcomprises transmitting the probe signal using an antenna, the methodfurther comprising: determining, with the antenna immersed in a firstmedium, a first input impedance of the antenna; determining, with theantenna immersed in a second medium, a second input impedance of theantenna; and determining a relative permattivity of the first mediumusing the first and second input impedances.
 12. The method of claim 1,wherein the first medium comprises substantially solid material, and thesecond medium comprises a fluid.
 13. The method of claim 1, furthercomprising producing a difference signal using the probe signal and thereturn signal, wherein storing the information further comprises storinginformation associated with the difference signal corresponding to theobject.
 14. The method of claim 13, further comprising applying a windowfunction to the difference signal, and range-gate filtering the windoweddifference signal.
 15. A system for detecting an object, comprising: atransmitter, coupled to an antenna, that transmits a frequency-modulatedprobe signal having a center frequency and a sweep bandwidth; areceiver, coupled to the antenna, that receives a return signalresulting from the probe signal; a frequency selector that controlsshifting of the probe signal center frequency to a number of centerfrequency values; a memory that stores information of the return signalresulting from transmission of the probe signal at each of the centerfrequency values; and a processor, coupled to the memory, that computesa range to the object using the information stored in the memory. 16.The system of claim 15, wherein the memory stores magnitude and phaseinformation of the return signal, and the processor computes the rangeto the object using the magnitude and phase information stored in thememory.
 17. The system of claim 15, further comprising a filter coupledto the antenna and the receiver that suppresses reflections from theantenna.
 18. The system of claim 17, wherein the filter operates as arange- gating filter.
 19. The system of claim 15, further comprising alinearizing circuit coupled to the processor, the linearizing circuitlinearizing a plurality of frequency steps over which the centerfrequency is shifted.
 20. The system of claim 19, wherein thelinearizing circuit comprises a digital synthesizer circuit.
 21. Thesystem of claim 15, wherein the frequency selector controls adjustmentof the sweep bandwidth.
 22. A system for detecting an object,comprising: means for transmitting a probe signal having a centerfrequency and a sweep bandwidth; means for receiving a return signalresulting from the probe signal; means for shifting the center frequencyto a number of center frequency values; memory for storing informationcorresponding to the object derived by using the return signal at eachof the center frequency values; and means for computing a range to theobject using the information stored in the memory.
 23. The system ofclaim 22, wherein the storing means comprises means for storingmagnitude and phase information corresponding to the object derived byusing the return signal.
 24. The system of claim 23, wherein thecomputing means comprises means for computing the range to the objectusing the stored magnitude and phase information.
 25. The system ofclaim 22, wherein the probe signal comprises a frequency-modulated probesignal.
 26. The system of claim 22, wherein the shifting means comprisesmeans for shifting the center frequency within a frequency range ofapproximately 2 GHz to approximately 18 GHz.
 27. The system of claim 22,wherein the shifting means comprises means for changing the sweepbandwidth.
 28. The system of claim 22, wherein the shifting meanscomprises means for linearizing a plurality of frequency steps overwhich the center frequency is shifted.
 29. The system of claim 22,further comprising means for range-gate filtering the return signal. 30.The system of claim 22, wherein the object is an underground object. 31.The system of claim 22, further comprising an antenna coupled to thetransmitting means and the receiving means, respectively, and the systemfurther comprises: means for determining, with the antenna immersed in afirst medium, a first input impedance of the antenna; means fordetermining, with the antenna immersed in a second medium, a secondinput impedance of the antenna; and means for determining a relativepermittivity of the first medium using the first and second inputimpedances.
 32. The system of claim 31, wherein the first mediumcomprises substantially solid material, and the second medium comprisesa fluid.
 33. The system of claim 22, further comprising means forproducing a difference signal using the probe signal and the returnsignal, wherein the storing means comprises means for storing theinformation associated with the difference signal corresponding to theobject.
 34. The system of claim 33, further comprising: means forapplying a window function to the difference signal; and means forrange-gate filtering the windowed difference signal.